Chiral-Anomaly-Induced Nonlinear Hall Effect in Tilted Weyl Semimetals

Abstract

Weyl semimetals (WSMs) are a newly discovered class of quantum materials which can host a number of massless quasiparticles called Weyl fermions. One of the most unique properties of WSMs is the chiral anomaly – a pair of Weyl nodes of opposite chirality acts as source and drain of electrons in the presence of non-perpendicular electric and magnetic fields. To date, the most remarkable phenomenon induced by the chiral anomaly is the longitudinal negative magnetoresistance, which is a linear response effect. In this work, we theoretically investigate the transport properties of WSMs in the nonlinear regime and predict a novel nonlinear Hall effect in tilted non-centrosymmetric Weyl semimetals. Intuitively, a steady-state density difference between a pair of Weyl nodes is established when the chiral pumping and internode relaxation reach a balance, which conspires with the anomalous velocity to give rise to this nonlinear Hall effect. Taking the semiclassical Boltzmann approach, we find that the nonlinear Hall conductivity scales linearly with both the electric and magnetic fields, and depends critically on the tilting of the Weyl cones in both type-I and type-II WSMs. For a pair of Weyl cones that are un-tilted or oppositely tilted, the chiral-anomaly-induced nonlinear Hall current vanishes because it is forbidden by a mirror symmetry. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was proposed to occur in time-reversal invariant materials [1].